Exam #3 solutions: (14 points) answer the following questions about approximation: (a) (7 points) choose x0 = 2 to be an initial approximation of. Newton"s method on an appropriately chosen polynomial function to develop x1, a better. 4 20; also give an arithmetic expression (which need not be rational approximation of simpli ed) for the better approximation x2 arising from a second step of newton"s method. We want an easy-to-evaluate polynomial of which 4 20 is a zero, in order for newton"s method to help us approximate it; the obvious choice is f (x) = x4 20. Then, x1 = x0 f (x0) f (x0) And we follow up with the further improvement. 157216, which is within 0. 00005 of the correct value of 4 20. x2 = x1 f (x1) f (x1) This last expression is far too complicated to easily simplify by hand, but it is actually.